Tetrahedron-like Pores in (100)-oriented GaAs

As it was already mentioned in Chapter 2 - Electrochemistry of semiconductors, the voltage drop across the semiconductor-electrolyte junction is a very important parameter and determines the reaction at the interface.

In Figure 3.10 a cross section was presented taken from a porous layer fabricated at a current density of 4 mA/cm². In that case, with the exception of the phase of pore nucleation (up to 5 min), the monitored voltage (under galvanostatic control) between the RE and SE electrodes has a relatively constant value during the whole experiment. As discussed, the pores are oriented along <111>B directions and possess a well developed triangular prism-like shape with {112} planes as facets [51, 62].

Figure 3.22: Time dependence of the measured voltage during the anodization process at different high external current densities: a) HCl 5%; b) HCl 10%. The time when the voltage jump occurs depends on the current density and electrolyte concentration. The increase in the external current density as well as the increase in the electrolyte concentration leads to the decrease in the time required to reach the conditions which cause the external voltage jump.

However, the time dependence of the RE-SE voltage shows some particular changes when the external current density is increased to higher values. After an initial interval of nearly constant voltage at the beginning of the etching process, during which the domains of crystallographically oriented pores develop and grow, a sharp increase in the monitored voltage occurs. At the current density j=85 mA/cm², for instance, a sharp voltage jump can be observed after approximately 75 min of etching in 5 % HCl electrolyte solution (see Figure 3.22). As proved by SEM investigations, this sudden change in the voltage across the semiconductor-electrolyte junction is a sign that a new pore growth phase started.

Figure 3.23: Examples of tetrahedron-like pores in GaAs; a) Tetrahedron-like pores obtained on (100)-oriented GaAs (n=10¹⁷ cm^-3) at high current densities j=85 mA/cm² in 5% HCl aqueous electrolytes after 75 minutes of anodization. They grow along <111>B directions similar with the usual crystallographically oriented pores; b) The tetrahedron-like pores expose the {111}A planes.

Figure 3.23 shows the SEM image of pores obtained after the voltage jump, taken in cross section from a sample anodized at a current density of 85 mA/cm². The pores still form an angle of 54.5^o with the normal to the surface, i.e. they continue to grow along <111>B directions as they did before the voltage jump. However, the pore walls are not smooth anymore as those presented in Figures 3.10, but show evident diameter modulations. The modulations look like chains of interconnected tetrahedral voids. Three of four facets of the tetrahedron can be easily observed in Figure 3.23b. Taking into account that no influence from exterior has been applied to the system during the etching process, this clearly indicates that a self-induced diameter oscillation of individual pores takes place at this stage of pore growth.

It is noteworthy to mention that a similar morphology has been observed in Si [63], but instead of tetrahedron-like voids an octahedron-like structure develops in Si. This difference is mainly due to the fact that the dissolution 'stopping planes' in Si are different from those in GaAs (see Figure 3.24 for comparison). In Si the growth of octahedron pores starts with a pyramid like cavity exposing four stable {111} planes. The tip of the pyramid is oriented along one of the <100> directions. In most cases this pyramid is simply sliding continuously along <100> directions forming pores with smooth walls. However, there are situations, determined certainly by the etching conditions, when the pyramid will not slide continuously along <100> directions but will move in 'steps' resulting in octahedron-shaped pores.

In the case of GaAs the situation is slightly different. Due to the difference in dissolution rates between {111}A and B planes, the pores will grow along <111>B directions. The tips of the pores will expose {111}A planes forming a tetrahedron-like cavity. A continuous sliding of the tetrahedron-like tip will generate smooth crystallographically oriented pores (see also section 3.3.1). However, a step-like movement of the tip will generate tetrahedron-like pores. A schematic mechanism and SEM pictures of tetrahedron- and octahedron-like pores in GaAs and Si are presented in Figure 3.24a and b [63].

Figure 3.24: Tetrahedron and octahedron-like pores in GaAs and Si. a) In GaAs four {111}A planes form a tetrahedron cavity which at high current density, after a certain period of time, will start to move in steps along <111>B directions. b) In Si, on the other hand, eight {111} planes form an octahedron cavity which moves in steps along the <100> direction. c,d) SEM pictures showing a direct comparison between the observed in GaAs and the similar octahedron-like pores observed in Si. This step-like moving is explained in the framework of the current burst model by means of the aging concept. The picture taken from octahedron-like pores in Si is reproduced with the kind permission of Dr. C. Jäger and Prof. Dr. W. Jäger, University of Kiel.

The observation of self-induced diameter oscillation, i.e. observation of tetrahedron and octahedron pores, in quite different semiconductors like Si and GaAs (see Figure 3.24c and d), indicates, that the general mechanism governing pore formation in these materials is more or less the same. In Si the observation of the octahedron-like pores was explained using the aging concept introduced by the current burst model. Thus, the same concept can be used to explain the formation of tetrahedron-like pores in GaAs.

Figure 3.25: A schematic representation of the process explaining the tetrahedron-like pore formation according to the 'aging' concept. Time t₁ - nearly the whole surface of the pore tip is passivated and a new tetrahedron starts to grow at the very tip of the pore (jtip jumps from the minimum to the maximum value). The new tetrahedron starts to grow as a small spherical cavity whose walls are not passivated at all. The current density is considered to be constant during this period. Time t₂ -The surface of the sphere (A_tip) and the current I=j×A_tip, which is flowing through it, will increase up to the maximum value - I_max (diffusion determined), which can be carried through one pore. Due to the fact that the sphere at some moment will begin to expose small areas of <111>A planes (which can be easily passivated) the current density will start to decrease until the surface will again be totally passivated and a new cycle will start.

In the framework of the current burst model, aging describes the passivation of pore tips as a function of time and current density. It is well known that H- passivation hinders the oxidation of Si and is strongly crystallography dependent. For example, {111} planes can be easily passivated as a consequence are most stable against dissolution. This explains also why in porous Si the observed octahedron-like pores expose {111} planes as most stable. The most stable planes are also called 'stopping planes'. However, in GaAs it is Cl- passivation rather than H- passivation which impedes oxidation and thus the process of local dissolution [55].

A schematic model of the process assumed to be responsible for the formation of tetrahedron-like pores in GaAs is presented in Figure 3.25. Consider the situation when the current density at a pore tip (j_tip) has reached a critical low value jmin where nearly the whole surface of the pore tip (A_tip) is passivated (t1 in Figure 3.25). The mechanism how the system reaches the critical current density will be explained later. Bearing in mind that the experiments were performed galvanostatically, the same current must flow through the sample all the time and in all conditions. Thus, it can happen that in order to maintain a constant high current through the whole sample the system will be forced to 'abandon' a significant part of the strongly passivated surface of the tip and to concentrate the current flow only through a small area at the tip in order to increase the current density, which in turn will decreas significantly the passivation (t=t1 in Figure 3.25). Therefore on the diagram in Figure 3.25 at t=t₁ sharp steps for S_tip (down) and j_tip (up) are sketched.

The reason why the system chooses the small area at the very tip is that here the electrical field strength is much higher, due to the curvature of the pore tip, and as a consequence, it is easier to break the passivation. Immediately after t₁ a small spherical cavity at the tip of the pore is formed (see the dash circle in Figure 3.23b). At this stage the cavity does not expose any crystallographic planes, no preferential passivation is present and the reaction on the surface of the cavity can be considered to be kinetically controlled. This means that due to dissolution the surface of the sphere will increase with time in a quadratic manner (a sphere), while the current density at the tip remains constant (t₁2 in Figure 3.25).

Consequently, during this period of time the value of the current (not to mix up with current density) I=jtip×Stip will increase as the surface does. Nevertheless, taking into account that tetrahedron-like pores begin to grow far below the surface, the current I will increase only up to a certain maximum value (I_max), which in fact is defined (limited) by the diffusion of the species (reducing, oxide dissolving and reaction products) to and from the pore tips. Because Imax is the maximum current value the system can transport through one pore, it will try to keep I=I_max constant for a while (t₂ < t < t₃). Since the surface of the sphere will continue to grow (dissolution takes place) the current density for this cavity starts to decrease and, according to the 'current-burst' model, the surface passivation will increase. Certainly the {111}A planes will be passivated more easily. Thus, after the current Imax (diffusion limited) is reached and the current density at the pore tip begins to decrease again, the spherical cavity will begin to expose these planes (t>t₂) transforming itself into a tetrahedron-like cavity. The current density jtip will continue to decrease until it reaches again the critical value and consequently, a new step in Atip and jtip will occur (t=t₄), i.e. a new tetrahedron begins to grow.

As it can be observed from Figure 3.25, the current at pore tips I varies in time, following the phase of the growth of the tetrahedrons. Note that within the framework of the 'current-burst' model one of the general assumptions is that the current at the pore tip also oscillates, but due to random phases of the oscillations at different pore tips a constant macroscopic current across the sample results.

This model allows one to explain two additional features:

• The tetrahedron-like pores are observed only after a definite interval of time from the beginning of the experiment. At the beginning of the experiment the current density at pore tips is much higher than the critical value j_min, therefore the system needs some time before reaching it by successive branching of the original pores (domain formation);
• The system can reach the critical current density at pore tips only at high externally applied currents. As discussed in Section 3.3.3, at high current densities the pores initially nucleated at the surface of the sample are branching and form domains. If a constant external current is applied to the sample, the current density at pore tips depends on the number of pore tips (pores) growing into the substrate. Thus, due to branching the number of pore tips in the substrate increases in time, which means that the current density at the pore tips is not constant but decreases in time. Eventually, the decrease of j_tip with time allows the system to reach the critical current density j_min at the pore tips, which leads to the formation of linked tetrahedrons as explained above. On the other hand, at low values of the external current the branching effect is practically absent or strongly reduced, therefore the number of pore tips is constant in time and so is the current density at the tips, i.e. it cannot decrease up to the critical value where the tetrahedron pores begin to grow. Also, the diffusion limited current I_max (extremely important for the model of tetrahedron formation) at low external current densities cannot be achieved because the amount of dissolved material is small as compared with the case of high external current densities.

In order to test experimentally the above assumptions, the influence of electrolyte concentration and current density on the time interval from the beginning of the experiment until tetrahedron-like pores begin to grow was investigated. Figure 3.22 shows the time dependence of the voltage at different current densities for two electrolyte concentrations, 5 % HCl (Figure 3.22a) and 10 % HCl (Figure 3.22b). The time needed for the system to reach the tetrahedron regime of pore growth shortens both by increasing the external current density and electrolyte concentration.

These observations can be explained by a higher passivation rate at higher concentration of Cl- ions in the electrolyte. During the anodization, comparable passivation states (equal number of passivated bonds on surface unit) for two different concentrations of the electrolyte c₁2, are obtained if the current densities that must flow through pore tips satisfy the relation j₁2. Consequently, the critical value j_min will be higher in more concentrated solutions ( j_min1min2). As explained above, the actual current density at pore tips decreases in time (due to branching) from the initial value j_init at the surface of the sample until j_min is reached and the system enters a new state indicated by the voltage jump. So, the time needed to reach jmin2 is shorter than that required to reach jmin1 because j_init-j_min2init-j_min1. This is in good agreement with the results presented in Figure 3.22a and b.

The decrease of time necessary for the system to reach the tetrahedron-like pore regime when increasing the externally applied current density can be explained if taking into account that branching of pores occurs more frequently at high externally applied currents and is nearly absent at low currents. Thus jtip decreases faster at high externally applied currents than at low ones. Consequently jmin is reached in a shorter period of time.

The observed architecture of pores offers new insights into the mechanism of pore formation in GaAs, and also represents an interesting variety of possible pore structures for applications. The pores obtained at high current densities after the voltage jump look like asymmetrically-modulated microchannels, and according to the concept of the drift ratchet [64], can be used for the purpose of designing micropumps to separate micrometer-size particles dissolved in liquids.